A quasi-deformation of \(R\)  is a diagram \(R\rightarrow A\twoheadleftarrow Q\)  of local homomorphisms, in which \(R\rightarrow A\)  is faithfully flat, and \(A\twoheadleftarrow Q\)  is surjective with kernel generated by a regular sequence. The complete intersection dimension of \(M\) , introduced by Avramov, Gasharov and Peeva [1]}, is:
\(\operatorname{\textnormal {CI-dim}}_R(M)=\inf \lbrace \operatorname{pd}_Q(M\otimes _RA)-\operatorname{pd}_Q(A)\mid R\rightarrow A\twoheadleftarrow Q \text{ is a quasi-deformation}\rbrace .\) 
